DS 6372 Project 1
World Health Organization
Context
Although there have been lot of studies undertaken in the past on factors affecting life expectancy considering demographic variables, income composition and mortality rates. It was found that affect of immunization and human development index was not taken into account in the past. Also, some of the past research was done considering multiple linear regression based on data set of one year for all the countries. Hence, this gives motivation to resolve both the factors stated previously by formulating a regression model based on mixed effects model and multiple linear regression while considering data from a period of 2000 to 2015 for all the countries. Important immunization like Hepatitis B, Polio and Diphtheria will also be considered. In a nutshell, this study will focus on immunization factors, mortality factors, economic factors, social factors and other health related factors as well. Since the observations this dataset are based on different countries, it will be easier for a country to determine the predicting factor which is contributing to lower value of life expectancy. This will help in suggesting a country which area should be given importance in order to efficiently improve the life expectancy of its population.
Column Names: Meanings
- Year: Year
- Status: Developed or Developing status
- Life expectancy: Life Expectancy in age
- Adult Mortality: Adult Mortality Rates of both sexes (probability of dying between 15 and 60 years per 1000 population)
- infant deaths: Number of Infant Deaths per 1000 population
- Alcohol: Alcohol, recorded per capita (15+) consumption (in litres of pure alcohol)
- percentage expenditure: Expenditure on health as a percentage of Gross Domestic Product per capita(%)
- Hepatitis B: Hepatitis B (HepB) immunization coverage among 1-year-olds (%)
- Measles:Measles - number of reported cases per 1000 population
- BMI: Average Body Mass Index of entire population
- Polio: Polio (Pol3) immunization coverage among 1-year-olds (%)
- Total expenditure: General government expenditure on health as a percentage of total government expenditure (%)
- Diphtheria: Diphtheria tetanus toxoid and pertussis (DTP3) immunization coverage among 1-year-olds (%)
- HIV/AIDS: Deaths per 1 000 live births HIV/AIDS (0-4 years)
- GDP: Gross Domestic Product per capita (in USD)
- Population: Population of the country
- thinness 1-19 years: Prevalence of thinness among children and adolescents for Age 10 to 19 (%)
- thinness 5-9 years: Prevalence of thinness among children for Age 5 to 9(%)
- income composition of resources: Human Development Index in terms of income composition of resources (index ranging from 0 to 1)
- schooling: Number of years of Schooling(years)
1. Does various predicting factors which has been chosen initially really affect the Life expectancy? What are the predicting variables actually affecting the life expectancy?
After running multiple regression models (forward, backward, and stepwise), it was determined that the following variables are the predictors that are statically significant in regards to life expectancy.
Variables - Adult.Mortality
- infant deaths - Total.expenditure - HIV.AIDS - Income.composition.of.resources
While the other variables intuitively may appear significant, the variables above are the predictors that have significant impact according to the regression models. interestingly enough, all models resulted in the same variables being returned.
##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + infant.deaths +
## under.five.deaths + Total.expenditure + HIV.AIDS + Income.composition.of.resources,
## data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.568 -1.569 -0.127 1.561 10.060
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 47.860575 2.066580 23.159 < 2e-16 ***
## Adult.Mortality -0.017405 0.003866 -4.502 1.53e-05 ***
## infant.deaths 0.042287 0.029527 1.432 0.154625
## under.five.deaths -0.033561 0.022614 -1.484 0.140331
## Total.expenditure 0.349095 0.111930 3.119 0.002258 **
## HIV.AIDS -0.809261 0.231621 -3.494 0.000661 ***
## Income.composition.of.resources 35.911609 2.502726 14.349 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.096 on 124 degrees of freedom
## Multiple R-squared: 0.8765, Adjusted R-squared: 0.8705
## F-statistic: 146.7 on 6 and 124 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + infant.deaths +
## Alcohol + percentage.expenditure + Hepatitis.B + Measles +
## BMI + under.five.deaths + Polio + Total.expenditure + Diphtheria +
## HIV.AIDS + GDP + Population + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Status_dc,
## data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.4098 -1.7264 -0.0392 1.7715 8.3880
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.122e+01 3.314e+00 15.457 < 2e-16 ***
## Adult.Mortality -1.724e-02 4.148e-03 -4.157 6.36e-05 ***
## infant.deaths 8.287e-02 5.619e-02 1.475 0.143057
## Alcohol 5.674e-03 9.749e-02 0.058 0.953689
## percentage.expenditure 4.627e-04 4.639e-04 0.997 0.320716
## Hepatitis.B 1.205e-02 2.808e-02 0.429 0.668582
## Measles -3.361e-05 4.823e-05 -0.697 0.487345
## BMI -7.576e-03 2.000e-02 -0.379 0.705531
## under.five.deaths -6.014e-02 3.838e-02 -1.567 0.119989
## Polio -8.746e-03 2.117e-02 -0.413 0.680327
## Total.expenditure 2.878e-01 1.274e-01 2.259 0.025833 *
## Diphtheria 7.644e-03 3.445e-02 0.222 0.824805
## HIV.AIDS -8.363e-01 2.470e-01 -3.385 0.000984 ***
## GDP -5.980e-05 6.656e-05 -0.898 0.370911
## Population -1.729e-09 6.804e-09 -0.254 0.799816
## thinness..1.19.years -1.300e-01 2.267e-01 -0.574 0.567462
## thinness.5.9.years 5.458e-03 2.227e-01 0.025 0.980489
## Income.composition.of.resources 3.597e+01 6.228e+00 5.775 7.11e-08 ***
## Schooling -1.617e-01 2.740e-01 -0.590 0.556279
## Status_dc -1.170e+00 1.035e+00 -1.130 0.261006
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.186 on 111 degrees of freedom
## Multiple R-squared: 0.8829, Adjusted R-squared: 0.8629
## F-statistic: 44.06 on 19 and 111 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + infant.deaths +
## under.five.deaths + Total.expenditure + HIV.AIDS + Income.composition.of.resources,
## data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.568 -1.569 -0.127 1.561 10.060
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 47.860575 2.066580 23.159 < 2e-16 ***
## Adult.Mortality -0.017405 0.003866 -4.502 1.53e-05 ***
## infant.deaths 0.042287 0.029527 1.432 0.154625
## under.five.deaths -0.033561 0.022614 -1.484 0.140331
## Total.expenditure 0.349095 0.111930 3.119 0.002258 **
## HIV.AIDS -0.809261 0.231621 -3.494 0.000661 ***
## Income.composition.of.resources 35.911609 2.502726 14.349 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.096 on 124 degrees of freedom
## Multiple R-squared: 0.8765, Adjusted R-squared: 0.8705
## F-statistic: 146.7 on 6 and 124 DF, p-value: < 2.2e-16
2.Should a country having a lower life expectancy value(<65) increase its healthcare expenditure in order to improve its average lifespan?
3.How does Infant and Adult mortality rates affect life expectancy?
4.Does Life Expectancy has positive or negative correlation with eating habits, lifestyle, exercise, smoking, drinking alcohol etc.
5.What is the impact of schooling on the lifespan of humans?
Life expectancy and schooling have a positive linear relationship. Despite not being significant in the full model, schooling is a significant indicator when its modeled as a singly linear regression.
The summary statistics shows high significants of alpha less than 0.001. The relationship can be modeled by the regression below:
life expectancy = 38.72 + 2.51(schooling)We notice that as schooling increases by a year, life expectancy is increased by 2.5 years, with no schooling having a life expectancy of 38.72 years.
##
## Call:
## lm(formula = Life.expectancy ~ Schooling, data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.6180 -3.2318 0.5415 3.3678 9.3898
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.7198 2.1350 18.14 <2e-16 ***
## Schooling 2.5086 0.1646 15.24 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.162 on 129 degrees of freedom
## Multiple R-squared: 0.6429, Adjusted R-squared: 0.6401
## F-statistic: 232.2 on 1 and 129 DF, p-value: < 2.2e-16
6.Does Life Expectancy have positive or negative relationship with drinking alcohol?
Life expectancy has a slight positive increase with alcohol consumption.
life expectancy = 67.11 + 1.11(Alcohol)Notice that as alcohol consumption incrases, life expectancy incrases by 1.11 years, starting at 67.11 years expected if no alcohol is consumed.
This is a bit counter intuitive considering the knowledge that alcohol is not considered to be healthy and many studies suggest that alcohol could shorten life spans. Keeping this in coonsideration, additional studies may need to be conducted.
##
## Call:
## lm(formula = Life.expectancy ~ Alcohol, data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.6896 -4.4306 0.8788 5.4897 15.8788
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.1100 0.8008 83.81 < 2e-16 ***
## Alcohol 1.1140 0.1571 7.09 7.89e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.328 on 129 degrees of freedom
## Multiple R-squared: 0.2804, Adjusted R-squared: 0.2748
## F-statistic: 50.26 on 1 and 129 DF, p-value: 7.887e-11
7.Do densely populated countries tend to have lower life expectancy?
Initally, there is a significant outlier that skews the data dramatically. Once removed, we noticed the sloped droped by nearly 50%. Considering that there is the possibility of having significanlt high populations, it has been concluded to keep the data point in.
life expectancy = 70.58 - 2.65(Population)Notice that as the population in a country increases, life expectancy decreases by 2.65 years, starting at 70.58 years expected if there is no population. In this scenario, the intercept independent of the slope has no logical reasoning considering that no population would result in no life expectancy.
##
## Call:
## lm(formula = Life.expectancy ~ Population, data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.477 -5.797 1.446 5.222 18.421
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.058e+01 7.680e-01 91.903 <2e-16 ***
## Population -2.654e-09 6.488e-09 -0.409 0.683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.633 on 129 degrees of freedom
## Multiple R-squared: 0.001295, Adjusted R-squared: -0.006447
## F-statistic: 0.1673 on 1 and 129 DF, p-value: 0.6832
##
## Call:
## lm(formula = Life.expectancy ~ Population, data = newdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.561 -5.546 1.635 5.137 18.332
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.067e+01 8.125e-01 86.978 <2e-16 ***
## Population -1.042e-08 2.306e-08 -0.452 0.652
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.662 on 128 degrees of freedom
## Multiple R-squared: 0.001592, Adjusted R-squared: -0.006208
## F-statistic: 0.204 on 1 and 128 DF, p-value: 0.6522
8.What is the impact of Immunization coverage on life Expectancy?
Reviewing the graphs, there does not appear to be a significant relationship between life expectancy and immunization.
!!!!!!!!!!! Additional EDA!!!!!!!!!!!!!!!!
##
## Call:
## lm(formula = Life.expectancy ~ ., data = df_immunizations)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.1505 -5.2695 0.7869 5.0334 19.8007
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.647e+01 3.028e+00 18.648 <2e-16 ***
## Hepatitis.B -9.120e-02 6.498e-02 -1.404 0.1629
## Measles -2.967e-05 7.101e-05 -0.418 0.6767
## Polio 1.172e-01 4.912e-02 2.385 0.0186 *
## Diphtheria 1.405e-01 7.928e-02 1.772 0.0789 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.962 on 126 degrees of freedom
## Multiple R-squared: 0.1702, Adjusted R-squared: 0.1438
## F-statistic: 6.46 on 4 and 126 DF, p-value: 9.221e-05
Objective 1
Display the ability to build regression models using the skills and discussions from Unit 1 and 2 with the purpose of identifying key relationships, interpreting those relationships, and making good predictions.
Reminder, key here is to tell a good story.
Build Model 1
- Identify key relationships
- Ensure interpretability
Unit 2 Objectives: - bias vs. variance - complexity - LASSO, LARS, CV (cross validation)
Perform regression analysis
- Report predictive ability
- Test/train set
- CV data
Hypothesis Testing
Interpret the coefficients
Confidence intervals
Practical and statistical significance
Model 2
- Product the best predictions as possible
- Interpretation is no longer required, hence complexity is no longer an issueFeature selection to avoid overfitting
Create the model
Compare model 1 vs. model 2
Comment on the differences of the models and whether model 2 brings any benefit
Objective 2
- Nonparametric technique
- kNN or regression trees (select one)Set of predictors from previous regression: (fill this out)
Model
A brief description of your nonparametric model’s strategy to make a prediction. Include Pros and Cons.
Provide any additional details that you feel might be necessary to report.
Report the test ASE using this nonparametric model so we can see how well it does compared to regression.
EDA
Suchi’s EDA
## Jamie’s EDA
Linear correlations: - Schooling vs Income.composition.of.resource - thinness..1.19.years vs thinness.5.9.years - life exp. vs schooling - life exp. vs income - infant death vs under 5 death
removed variables that were correlated
## Country Year Status Life.expectancy
## Afghanistan : 1 Min. :2014 Developed : 32 Min. :48.10
## Albania : 1 1st Qu.:2014 Developing:151 1st Qu.:65.60
## Algeria : 1 Median :2014 Median :73.60
## Angola : 1 Mean :2014 Mean :71.54
## Antigua and Barbuda: 1 3rd Qu.:2014 3rd Qu.:76.85
## Argentina : 1 Max. :2014 Max. :89.00
## (Other) :177
## Adult.Mortality infant.deaths Alcohol percentage.expenditure
## Min. : 1.0 Min. : 0.00 Min. : 0.010 Min. : 0.00
## 1st Qu.: 66.0 1st Qu.: 0.00 1st Qu.: 0.010 1st Qu.: 11.06
## Median :135.0 Median : 2.00 Median : 0.320 Median : 151.10
## Mean :148.7 Mean : 24.56 Mean : 3.271 Mean : 1001.91
## 3rd Qu.:216.5 3rd Qu.: 18.00 3rd Qu.: 6.700 3rd Qu.: 703.21
## Max. :522.0 Max. :957.00 Max. :15.190 Max. :19479.91
## NA's :1
## Hepatitis.B Measles BMI under.five.deaths
## Min. : 2.00 Min. : 0 Min. : 2.00 Min. : 0.00
## 1st Qu.:79.00 1st Qu.: 0 1st Qu.:23.20 1st Qu.: 0.00
## Median :93.00 Median : 13 Median :47.40 Median : 3.00
## Mean :83.12 Mean : 1831 Mean :41.03 Mean : 32.89
## 3rd Qu.:97.00 3rd Qu.: 316 3rd Qu.:59.80 3rd Qu.: 22.00
## Max. :99.00 Max. :79563 Max. :77.10 Max. :1200.00
## NA's :10 NA's :2
## Polio Total.expenditure Diphtheria HIV.AIDS
## Min. : 8.00 Min. : 1.210 Min. : 2.00 Min. :0.100
## 1st Qu.:80.00 1st Qu.: 4.480 1st Qu.:83.00 1st Qu.:0.100
## Median :94.00 Median : 5.840 Median :94.00 Median :0.100
## Mean :84.73 Mean : 6.201 Mean :84.08 Mean :0.682
## 3rd Qu.:97.00 3rd Qu.: 7.740 3rd Qu.:97.00 3rd Qu.:0.400
## Max. :99.00 Max. :17.140 Max. :99.00 Max. :9.400
## NA's :2
## GDP Population thinness..1.19.years
## Min. : 12.28 Min. :4.100e+01 Min. : 0.100
## 1st Qu.: 617.99 1st Qu.:2.869e+05 1st Qu.: 1.500
## Median : 3154.51 Median :1.568e+06 Median : 3.300
## Mean : 10015.57 Mean :2.106e+07 Mean : 4.533
## 3rd Qu.: 8239.95 3rd Qu.:8.080e+06 3rd Qu.: 6.600
## Max. :119172.74 Max. :1.294e+09 Max. :26.800
## NA's :28 NA's :41 NA's :2
## thinness.5.9.years Income.composition.of.resources Schooling
## Min. : 0.100 Min. :0.3450 Min. : 4.90
## 1st Qu.: 1.500 1st Qu.:0.5700 1st Qu.:10.80
## Median : 3.400 Median :0.7220 Median :13.00
## Mean : 4.676 Mean :0.6884 Mean :12.89
## 3rd Qu.: 6.600 3rd Qu.:0.7960 3rd Qu.:14.90
## Max. :27.400 Max. :0.9450 Max. :20.40
## NA's :2 NA's :10 NA's :10
## Life.expectancy.1 Status_dc
## Length:183 Min. :0.0000
## Class :character 1st Qu.:1.0000
## Mode :character Median :1.0000
## Mean :0.8251
## 3rd Qu.:1.0000
## Max. :1.0000
## ## [1] "Country" "Year"
## [3] "Status" "Life.expectancy"
## [5] "Adult.Mortality" "infant.deaths"
## [7] "Alcohol" "percentage.expenditure"
## [9] "Hepatitis.B" "Measles"
## [11] "BMI" "under.five.deaths"
## [13] "Polio" "Total.expenditure"
## [15] "Diphtheria" "HIV.AIDS"
## [17] "GDP" "Population"
## [19] "thinness..1.19.years" "thinness.5.9.years"
## [21] "Income.composition.of.resources" "Schooling"
## [23] "Life.expectancy.1" "Status_dc"
#### Regression Testing/Variables Reduction
Forward, backward, and stepwise regressions were run and all 3 resulted with the same 4 significant variables.
Variables - Adult.Mortality
- infant deaths - Total.expenditure - HIV.AIDS - Income.composition.of.resources
##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + Total.expenditure +
## HIV.AIDS + Income.composition.of.resources + Life.expectancy.1,
## data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.7539 -1.5929 0.0074 1.6631 10.6939
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 50.76505 2.32027 21.879 < 2e-16 ***
## Adult.Mortality -0.01700 0.00378 -4.496 1.56e-05 ***
## Total.expenditure 0.39230 0.10971 3.576 0.000497 ***
## HIV.AIDS -0.55729 0.24900 -2.238 0.026985 *
## Income.composition.of.resources 31.75821 2.96054 10.727 < 2e-16 ***
## Life.expectancy.1Low -2.90429 1.08518 -2.676 0.008441 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.029 on 125 degrees of freedom
## Multiple R-squared: 0.8809, Adjusted R-squared: 0.8761
## F-statistic: 184.9 on 5 and 125 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + infant.deaths +
## Alcohol + percentage.expenditure + Hepatitis.B + Measles +
## BMI + under.five.deaths + Polio + Total.expenditure + Diphtheria +
## HIV.AIDS + GDP + Population + thinness..1.19.years + thinness.5.9.years +
## Income.composition.of.resources + Schooling + Life.expectancy.1,
## data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.6206 -1.7993 0.1196 1.4778 9.0945
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.416e+01 3.441e+00 15.739 < 2e-16 ***
## Adult.Mortality -1.707e-02 4.062e-03 -4.201 5.39e-05 ***
## infant.deaths 5.084e-02 5.664e-02 0.897 0.371396
## Alcohol 5.116e-02 9.458e-02 0.541 0.589625
## percentage.expenditure 3.714e-04 4.545e-04 0.817 0.415602
## Hepatitis.B -8.781e-03 2.818e-02 -0.312 0.755941
## Measles -2.284e-05 4.748e-05 -0.481 0.631396
## BMI -7.922e-03 1.954e-02 -0.406 0.685872
## under.five.deaths -3.548e-02 3.892e-02 -0.912 0.363915
## Polio -7.978e-03 2.073e-02 -0.385 0.701115
## Total.expenditure 3.129e-01 1.243e-01 2.518 0.013221 *
## Diphtheria 2.522e-02 3.397e-02 0.742 0.459403
## HIV.AIDS -5.789e-01 2.628e-01 -2.202 0.029702 *
## GDP -2.934e-05 6.516e-05 -0.450 0.653446
## Population -2.321e-09 6.646e-09 -0.349 0.727600
## thinness..1.19.years 1.896e-02 2.296e-01 0.083 0.934327
## thinness.5.9.years -1.528e-01 2.261e-01 -0.676 0.500610
## Income.composition.of.resources 2.717e+01 7.106e+00 3.824 0.000217 ***
## Schooling 2.068e-02 2.732e-01 0.076 0.939815
## Life.expectancy.1Low -3.215e+00 1.303e+00 -2.468 0.015113 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.12 on 111 degrees of freedom
## Multiple R-squared: 0.8877, Adjusted R-squared: 0.8685
## F-statistic: 46.2 on 19 and 111 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Life.expectancy ~ Adult.Mortality + Total.expenditure +
## HIV.AIDS + Income.composition.of.resources + Life.expectancy.1,
## data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.7539 -1.5929 0.0074 1.6631 10.6939
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 50.76505 2.32027 21.879 < 2e-16 ***
## Adult.Mortality -0.01700 0.00378 -4.496 1.56e-05 ***
## Total.expenditure 0.39230 0.10971 3.576 0.000497 ***
## HIV.AIDS -0.55729 0.24900 -2.238 0.026985 *
## Income.composition.of.resources 31.75821 2.96054 10.727 < 2e-16 ***
## Life.expectancy.1Low -2.90429 1.08518 -2.676 0.008441 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.029 on 125 degrees of freedom
## Multiple R-squared: 0.8809, Adjusted R-squared: 0.8761
## F-statistic: 184.9 on 5 and 125 DF, p-value: < 2.2e-165.What is the impact of schooling on the lifespan of humans?
##
## Call:
## lm(formula = Life.expectancy ~ Schooling, data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.6180 -3.2318 0.5415 3.3678 9.3898
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.7198 2.1350 18.14 <2e-16 ***
## Schooling 2.5086 0.1646 15.24 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.162 on 129 degrees of freedom
## Multiple R-squared: 0.6429, Adjusted R-squared: 0.6401
## F-statistic: 232.2 on 1 and 129 DF, p-value: < 2.2e-166.Does Life Expectancy have positive or negative relationship with drinking alcohol?
Life expectancy has a slight positive increase with alcohol consumption.
##
## Call:
## lm(formula = Life.expectancy ~ Alcohol, data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.6896 -4.4306 0.8788 5.4897 15.8788
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.1100 0.8008 83.81 < 2e-16 ***
## Alcohol 1.1140 0.1571 7.09 7.89e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.328 on 129 degrees of freedom
## Multiple R-squared: 0.2804, Adjusted R-squared: 0.2748
## F-statistic: 50.26 on 1 and 129 DF, p-value: 7.887e-117.Do densely populated countries tend to have lower life expectancy?
##
## Call:
## lm(formula = Life.expectancy ~ Population, data = df1_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.477 -5.797 1.446 5.222 18.421
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.058e+01 7.680e-01 91.903 <2e-16 ***
## Population -2.654e-09 6.488e-09 -0.409 0.683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.633 on 129 degrees of freedom
## Multiple R-squared: 0.001295, Adjusted R-squared: -0.006447
## F-statistic: 0.1673 on 1 and 129 DF, p-value: 0.6832##
## Call:
## lm(formula = Life.expectancy ~ Population, data = newdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.561 -5.546 1.635 5.137 18.332
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.067e+01 8.125e-01 86.978 <2e-16 ***
## Population -1.042e-08 2.306e-08 -0.452 0.652
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.662 on 128 degrees of freedom
## Multiple R-squared: 0.001592, Adjusted R-squared: -0.006208
## F-statistic: 0.204 on 1 and 128 DF, p-value: 0.65228.What is the impact of Immunization coverage on life Expectancy?
Reviewing the graphs, there does not appear to be a significant relationship between life expectancy and immunization.
!!! Testing !!! - interaction terms - awknowledge polio significance
##
## Call:
## lm(formula = log.Life.expectancy ~ log.Hepatitis.B, data = df_immunizations)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37943 -0.07283 0.02674 0.07583 0.23398
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.10595 0.07087 57.939 <2e-16 ***
## log.Hepatitis.B 0.03321 0.01635 2.031 0.0443 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1242 on 129 degrees of freedom
## Multiple R-squared: 0.031, Adjusted R-squared: 0.02349
## F-statistic: 4.127 on 1 and 129 DF, p-value: 0.04426
